Write the eccentricity of the ellipse `9x^2+5y^2-18 x-2y-16=0.`

Explanation

`9 x^{2}+5 y^{2}-18 x-2 y-16=0`

`Rightarrow 9(x^{2}-2 x)+5(y^{2}-frac{2 y}{5})=16`

`Rightarrow 9(x^{2}-2 x+1)+5(y^{2}-frac{2 y}{5}+frac{1}{25})=16+9+frac{1}{5}`

`Rightarrow 9(x-1)^{2}+5(y-frac{1}{5})^{2}=frac{126}{5}`

`Rightarrow frac{(x-1)^{2}}{frac{126}{45}}+frac{(y-frac{1}{5})^{2}}{frac{126}{25}}=1`

`Rightarrow a^{2}=frac{126}{45}` and `b^{2}=frac{126}{25}`

Clearly,`a
Now,`e=sqrt{1-frac{a^{2}}{b^{2}}}`

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